When Fry and Bender are redecorating the apartment, they take down a Slurm painting that is a homage to Andy Warhol.
One of the apartment renters has a cell phone which chirps exactly like a communicator from Star Trek, the apartment door sounds like the doors on Star Trek as well.
Bender's apartment number, 00100100, when converted from binary to numerical value is 36 or the ASCII character "$". His neighbor, 00111001, is the number 57 or the ASCII number 9, and the apartment across the hall, 00100011, is 35 or the symbol "#".
When Bender bends Fry's alarm clock and drapes it over the edge of the table, the image is a reference to Salvador Dalí's "soft watches", which first appeared in his famous 1931 painting La persistencia de la memoria (The Persistence of Memory).
When Bender becomes sober he walks down the street and all these neon signs are going by. This is a reference to the 1945 film The Lost Weekend, where the main character walks down the street, drunk and all these neon signs pass by him.